Inelastic interaction of nearly equal solitons for the quartic gKdV equation

Yvan Martel (1, 2) , Frank Merle (3, 4)

1 LMV - Laboratoire de Mathématiques de Versailles
2 IUF - Institut universitaire de France
3 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
4 IHES - Institut des Hautes Études Scientifiques

This paper presents a complete description of the interaction of two solitons with nearly equal speeds for the quartic (gKdV) equation. By constructing an approximate solution of the problem, we prove that at the main order, the two solitons are preserved by the interaction and that for all time they are separated by a large distance, as in the case of the integrable KdV equation in this regime. However, unlike in the integrable case, we prove that the collision is not perfectly elastic.

Domaines: Equations aux dérivées partielles [math.AP]

Yvan Martel, Frank Merle. Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Inventiones Mathematicae, 2011, 183 (3), pp.563-648. ⟨10.1007/s00222-010-0283-6⟩. ⟨hal-00672816⟩